The present invention relates to a vibration removing apparatus particularly suitable to be used as a unit constituting an exposure apparatus in a semiconductor manufacturing apparatus having an XY platform. More particularly, the present invention relates to an improvement of an air-spring vibration removing apparatus which is capable of effective suppression of vibrations caused by movement of a device that is placed on the exposure apparatus.
Generally, devices that are susceptible to vibrations such as an optical microscope or an XY platform for exposure are placed on a vibration removing table of a vibration removing apparatus. Particularly for an XY platform used for exposure, vibrations externally transmitted must be removed from a vibration removing table as much as possible. This is because the XY platform for exposure must be still when exposure is executed.
Further, attention must be to the intermittent operation of an XY platform for exposure, called a "step & repeat" operation, which repeatedly generates step vibrations on its own and to the vibrations generated by the "step & repeat" operation on the vibration removing table.
An exposing operation should not be started before such vibrations are removed. Therefore, for a vibration removing table, removal of externally transmitted vibrations and controlling of forced vibrations caused by movement of a device placed on the vibration removing table must be balanced.
As a vibration removing table, a passive vibration removing table and an active vibration removing table are known. Lately, an active vibration removing table is more frequently used in order to satisfy the need for precise positioning, precise scanning and fast movement.
For an actuator used for an active vibration removing apparatus, there are an air-spring, a voice-coil actuator and a piezoelectric element. The present invention relates to an air-spring vibration removing apparatus utilizing an air-spring as an actuator and a description thereof will be provided below.
FIG. 3 shows a structure of a conventional air-spring vibration removing apparatus. In FIG. 3, reference numeral 1 denotes an air-spring supporting leg; 2 denotes a servo-valve for aspirating and evacuating air which functions as an operation fluid of an air spring 3; 4 denotes a position sensor for measuring a vertical displacement of a vibration removing table 5; 6 denotes a pressurizing mechanical spring, 7 denotes a viscosity element for expressing viscosity of the air spring 3, for the pressurizing mechanical spring 6, and for an entire structure (not shown); 8 denotes a feedback apparatus; 9, an acceleration sensor; 10 denotes a filter comprising a low-pass filter and a band-pass filter; 11 denotes a voltage-current converter; 12 denotes a displacement amplifier, 13 denotes a comparator, 14 denotes a reference voltage; and 15 denotes a PI compensator. Hereinafter, the combination of the air-spring supporting leg 1 and the feedback apparatus 8 will be referred to as an air-spring vibration removing apparatus. For the purpose of a simple explanation, only one vertical axis is illustrated for the air-spring vibration removing apparatus. The structure of the apparatus is identical in the horizontal direction. An apparatus structured with a plurality of the air-spring supporting legs 1 and a plane plate placed on each of the vibration removing table 5 is also referred to as an air-spring vibration removing apparatus.
Next, the structure and the operation of the feedback apparatus 8 for the air-spring supporting leg 1 will be described. An output of the acceleration sensor 9 is inputted as a negative feedback circuit to a preceding stage of the voltage-current converter 11, which generates current for opening and closing of the servo-valve 2 via the filter 10 having an appropriate amplification and a time constant. The mechanism is stabilized by the acceleration feedback loop. In other words, damping is provided. Further, an output of the position sensor 4 is sent through the displacement amplifier 12 and inputted to the comparator 13. The comparator 13 compares an output of the displacement amplifier 12 with the reference voltage 14, which is equivalent to the target position of the vibration removing table 5, and an error signal e is outputted. This error signal e is sent through the PI compensator 15 to obtain a control voltage and inputted to the voltage-current converter 11. The voltage-current converter 11 outputs a current corresponding to the control voltage, control opening and closing of the servo-valve 2, and adjusts the pressure of the air spring 3. As a result, the vibration removing table 5 is maintained at a desired position that has been designated by the reference voltage 14 without a steady-state error. Herein, "P" in the PI compensator 15 denotes a proportional action and "I", an integral action.
When a device placed on the vibration removing table 5 repeats intermittent operations, the reaction force thereof causes vibrations on the vibration removing table 5. Since the patterns of the intermittent operations of the placed device are already known, an appropriate compensation is applied to a driving signal which drives the intermittent operations and an output thereof is feedforwarded to the air spring 3 which is an actuator of the vibration removing table 5, in order to suppress vibrations of the vibration removing table 5.
As prior art, Japanese Patent Application Laid-Open (KOKAI) No. 6-216003 (entitled "Stage Device") and Japanese Patent Application Laid-Open (KOKAI) No. 6-81158 (entitled "Controller of Vibration-Removing Table") are known.
Japanese Patent Application Laid-Open (KOKAI) No. 6-216003 discloses a general concept in which displacement information of an XY platform is provided from an XY platform control portion to a vibration-removing control portion of a vibration-proof platform control system, and vibrations of the vibration-proof platform, caused by an operation of the XY platform placed on the vibration-proof platform, are controlled. Herein, the vibration-proof platform is what is called the vibration removing table in the present specification. The displacement information of the XY platform includes information, such as coordinates of the XY platform measured by a laser interferometer, velocity data of the XY platform based on each velocity data generated by a driving motor, and a driving voltage provided to the driving motor.
This conventional art discloses the concept of obtaining information from a signal driving the XY platform to control vibrations of the vibration removing table; however, no concrete structure of an apparatus is disclosed which explains how the information is processed to control vibrations of the vibration removing table.
Japanese Patent Application Laid-Open (KOKAI) No. 6-181158 suggests a control apparatus of an air-spring vibration removing table where a pseudo-differentiator is applied to a driving signal which is to be sent to a device placed on the vibration removing table 5; and an output signal thereof is lead to a supporting-input-terminal, which is arranged in a preceding stage of the current-voltage converter 11, which drives the servo valve 2, in order to control vibrations of the vibration removing table 5 caused by motion of the device. Described hereinafter is a theory of feedforward compensation based on a driving signal of a placed device to be applied to vibrations of a vibration removing table.
FIG. 4 shows a servo block diagram of the conventional air-spring vibration removing apparatus illustrated in FIG. 3. Referring to the reference numerals in FIG. 4, a relationship among a displacement x, a reference value r.sub.o, a disturbance f.sub.dis and a supporting input v.sub.FF can be expressed as follows. ##EQU1## x[m]: displacement (derived from the position sensor 4) r.sub.o [V]: reference value (reference voltage 14)
f.sub.dis [N]: disturbance PA0 v.sub.FF [V]: supporting input PA0 M[kg]: mass of vibration removing table 5 and placed device PA0 C[Ns/m]: viscosity friction coefficient PA0 K [N/m]: rigidity coefficient PA0 K.sub.I [Ns/V]: integration gain including the characteristics of the voltage-current amplifier 11 and the servo valve 2 PA0 K.sub.a [Vs.sup.2 /m]: acceleration feedback gain of the filter 10 PA0 K.sub.p [V/m]: gain of the displacement amplifier 12 PA0 T'[s]: a time constant of the PI compensator 15 PA0 .delta.[V/V]: position gain PA0 s: Laplace operator
The area indicated by the broken line in FIG. 4 includes both characteristics of the servo valve 2 and a mechanism. A transfer function thereof is expressed below. ##EQU2##
When an acceleration feedback is inputted, a transfer function from V.sub.c to displacement x is expressed as follows. ##EQU3##
It is clear from this equation that the acceleration feedback gain K.sub.a has a function to stabilize the entire mechanism by increasing the viscosity term.
The reference v.sub.FF denotes a voltage to be impressed to a supporting input in order to remove or decrease the effect on the displacement x caused by the disturbance f.sub.dis. Herein, the second term of the equation 1 can be canceled by the third term if a signal waveform of the supporting input v.sub.FF is adjusted.
The disturbance f.sub.dis is caused by a driven device placed on a vibration removing table. A waveform thereof is generally a bang-bang waveform as shown in FIG. 5. The waveform is caused by the placed device which is positioned after rapid speed adjustment is made. The bang-bang waveform can be expressed by a combination of step waveforms. Herein, suppose the disturbance f.sub.dis is a step waveform. Since a device placed on the vibration removing table 5 is driven by an actuator such as a DC servo-motor, an electric signal generated at the time of driving the actuator can be utilized as a signal corresponding to a disturbance f.sub.dis even when it is impossible to directly measure the disturbance f.sub.dis. This electric signal can be also utilized as an input to the supporting input v.sub.FF. However, the order of the polynomials in the numerators of the second and third terms of the equation 1 is 2 and 1 respectively. When a step-type disturbance f.sub.dis is inputted, impressing of the step-type voltage v.sub.FF would not remove the effects on the displacement x caused by including dynamics. Therefore, a signal inputted to the supporting input, v.sub.FF '=sv.sub.FF is newly inputted to the third term of the equation 1. However, the use of a differentiator which amplifies high-frequency noise is not preferable. In practice, a low-pass filter having an appropriate time constant T is added as a pseudo-differentiator, and feedforward compensation is executed through the pseudo-differentiator. The resulting relationship of the equation 1 is expressed in the equation 5. Note that k is the gain of the pseudo-differentiator. ##EQU4##
The idea of the above described feedforward compensation is to impress a signal v.sub.FF which cancels the effects of the disturbance f.sub.dis.
The effects of the aforementioned feedforward compensation for suppressing vibrations of the vibration removing table will be described below. The disturbance f.sub.dis is a bang-bang waveform as illustrated in FIG. 5. Suppose that the bang-bang waveform is repeatedly and periodically impressed. A comparison made between the displacement x with the supporting input v.sub.FF as described in the third term of the equation 5 and the displacement x without any supporting input is illustrated in FIGS. 6A and 6B. FIG. 6A illustrates a case where the supporting input v.sub.FF is impressed (with a feedforward compensation) and FIG. 6B illustrates the case where v.sub.FF =0 (without feedforward compensation). Obviously, the displacement x is more effectively suppressed in FIG. 6A compared with that of FIG. 6B. This experiment demonstrates the effectiveness of feeding a driving signal, which is to be sent to the device placed on the vibration removing table of the air-spring supporting leg, to the pseudo-differentiator, and impressing an output signal thereof to a preceding stage of the voltage-current converter 11 which drives a servo-valve. The experiment shown in FIG. 6 is a case where a setting of a closed-loop system, consisting of an air-spring supporting leg and a corresponding feedback apparatus, is excellent; more specifically, the period and the repetition of the disturbance f.sub.dis itself in the bang-bang waveform are relatively long compared to the natural period of the closed-loop system.
When a relationship of the above described natural period is reversed, for instance, when a subject supported by the vibration removing table 5 is large, the response of the air-spring vibration removing apparatus becomes slow. In other words, the natural period of the vibration removing table 5 becomes substantially long. On the other hand, motion patterns of a device placed on the vibration removing apparatus 5 becomes faster with a rapid short-period speed adjustment motion and its repeating period becomes shorter. A result of the experiment is shown in FIGS. 7 and 8 in which the above described feedforward compensation is executed by having a driving signal sent through a pseudo-differentiator for the vibration removing table 5. FIG. 7 shows the case without a feedforward compensation and FIG. 8 shows the case with the feedforward compensation. Although the vibration removing apparatus is completely different from the one utilized in FIG. 6, the control system is equivalent. In FIGS. 7 and 8, the waveforms A and A' indicate a displacement x, and waveforms B indicates a driving signal of a placed device. When the waveform A of the displacement x without a feedforward compensation is compared with the waveform A' with a feedforward compensation of a driving signal which has been pseudo-differentiated, a reduced amplitude of the displacement x is seen in a time domain of an initial positive edge of the driving signal B. However, within a time domain where the driving signal B has a negative polarity, an increased amplitude of the displacement x results when a feedforward compensation is applied thereto. The cause is apparent. It is because the response of the closed-loop in the air-spring vibration removing apparatus is substantially slower compared to the period of motion patterns of a device placed thereon, that is the period of positive-negative change of the bang-bang waveform shown in FIG. 5. An initial stage of an amplitude in the response waveform is suppressed by having a pulse signal, obtained by applying a pseudo-differentiator to a first positive edge of the bang-bang waveform, inputted to the voltage-current converter. However, since the suppressed waveform converges slowly, the negative edge of the waveform in a negative polarity of the bang-bang waveform and a positive edge of the following waveform are respectively inputted before the waveform converges to a steady state, resulting an increased response amplitude.
FIG. 9 is an example of numerical calculations that demonstrates the qualitative tendency of the above-described experiment. In FIG. 9, a solid line denotes a response without feedforward compensation, and a broken line denotes a response with feedforward compensation. In the case where the feedforward compensation is applied, the first peak value is suppressed to a low value compared with the case where a feedforward compensation is not applied, and a consecutive response waveform is extended, resulting a slowly converging waveform. Therefore, the numerical experiment proves that the result qualitatively coincides with the result of the experiment shown in FIGS. 7 and 8.
As set forth above, for an air-spring vibration removing apparatus having an air-spring as an actuator, an air-spring vibration removing apparatus has been suggested, wherein a signal obtained by pseudo-differentiating a speed-adjusting signal of a device placed on a vibration removing table is inputted as a feedforward compensation in a preceding stage of a voltage-current converter, which drives a servo-valve for adjusting air as an operation fluid of the air spring, in order to suppress vibrations caused by a positioning motion of a device placed on the apparatus. However, there is a drawback in that feedforward compensation for suppressing vibrations of the vibration removing table does not effectively function when the period of speed adjustment as well as a repeating period of the speed adjustment of the device placed on the air-spring vibration removing apparatus become substantially short, compared to the natural period of the air-spring vibration removing apparatus.